If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?
A. 10
B. 12
C. 14
D. 16
E. 18
A. 10
B. 12
C. 14
D. 16
E. 18
p = 1*2*3*...*29*30 = 30!diehard_gmat wrote:If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of p?
A. 10
B. 12
C. 14
D. 16
E. 18
The problem is basically asking us to find the number of 3's in p.
Now all the multiples of 3 (3, 6, ... , 30) has one 3 in them.
Number of multiples of 3 within 30 = 10
But 9 and 18 each has one extra 3 in them and 27 has two extra 3 in it.
Hence, total number of 3's in p = 10 + 1 + 1 + 2 = 14
The correct answer is C.
